Which of the following numbers is a multiple of 4? ${49,59,69,72,109}$
Answer: The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $49 \div 4 = 12\text{ R }1$ $59 \div 4 = 14\text{ R }3$ $69 \div 4 = 17\text{ R }1$ $72 \div 4 = 18$ $109 \div 4 = 27\text{ R }1$ The only answer choice that leaves no remainder after the division is $72$ $ 18$ $4$ $72$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $72$ $72 = 2\times2\times2\times3\times3 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $72$. We can say that $72$ is divisible by $4$.